Any paternity testing without a court order is banned, due to the official desire to "preserve the peace" within French families, with the French government citing psychologists who state that fatherhood is determined by society rather than biology. French men often circumvent these laws by sending samples of DNA to foreign laboratories, but risk prosecution if caught. The maximum penalty for carrying out secret paternity testing is one year in prison and a 15,000-Euro fine.[10][11]

http://en.wikipedia.org/wiki/Paternal_testing#France

If those samples were found in the post by officials on their way to foreign laboratories, the French men who sent them could theoretically face a year in prison and a 15,000 Euro fine. This year the ban was challenged but the French Government decided to uphold and maintain the anti-paternity testing law.

The reasons for which the Government said the ban should remain were related to the preservation of peace within French families. According to some online articles, Germany, has also banned (or plans to ban) paternity testing for similar reasons. French psychologists suggest that fatherhood is determined by society not by biology.

http://www.ibdna.com/regions/UK/EN/?page=paternity-testing-ban-upheld-in-france